1. Make aioli in a food processor or mixing bowl by combining mayonnaise, cayenne, and garlic. Cut the baguette lengthwise and slather generously with aioli'.
2. Toss avocado slices with lime juice, salt, and pepper. Spread into an even layer on the bottom of the French bread. Next, layer on the center-cut slices of tomato.
3. Close the sandwich, and divide with a sharp knife into 4 equal portions.